570 in the area of B that is not in A
At least 340 in the area of B that is shared with A
760 in B in total

That is not possible

Nov 26th 2011, 11:01 PM

Annatala

Re: Cardinalities and ultimate sets

You are correct. As stated, the problem is not possible, because there would have to be negative 150 people with mortgages and cars but no electricity. Either the problem is wrong, or you typed it in wrong.

Nov 27th 2011, 07:06 AM

ehpoc

Re: Cardinalities and ultimate sets

Here is the exact problem copy and pasted from the assignment. Can yo confirm I am not crazy and that there is indeed a typo?

Quote:

3. In a sample of 1000 cottage owners, 570 owned their cottages with no mortgage and also owned cars; 340 owned mortgaged cottages, owned cars, and had electricity; 189 had neither mortgages nor cars nor electricity; 760 owned cars. Find the cardinalities of the ultimate sets.

Nov 27th 2011, 09:41 AM

CaramelCardinal

Re: Cardinalities and ultimate sets

If that's the entire problem and there is no other information given in relation to the problem, then there is a typo.

Nov 27th 2011, 04:11 PM

ehpoc

Re: Cardinalities and ultimate sets

Is the problem these 3 premesis?

-570 in the area of B that is not in A
-At least 340 in the area of B that is shared with A
-760 in B in total

Nov 27th 2011, 04:18 PM

Annatala

Re: Cardinalities and ultimate sets

Quote:

Originally Posted by ehpoc

Is the problem these 3 premesis?

Yes. Simple math tells you that 910 > 760, so the only way to fit in the extra people is to cancel them out with negative people, which (unless you're looking at a time series change or something, perhaps that's the ticket) is impossible.

Nov 29th 2011, 10:52 AM

ehpoc

Re: Cardinalities and ultimate sets

Apparently the question intentionally uses improper data and the cardinality of the ultimate sets is a way to detect it....

So I am guess the set of A intersect B is going to be negative or something.

I still have no clue how I can find the cardinality of all of the ultimate sets from the information given.

Nov 29th 2011, 10:58 AM

Annatala

Re: Cardinalities and ultimate sets

If negative values are permitted, then it is not remotely possible to determine the number in each section of the Venn diagram with the information you have. For a solution to be possible, you would need at least 8 numbers given to you by the problem (with the correct overlaps), and you don't have 8 numbers, so it's impossible.

Also, please don't say "cardinality of set" if you're talking about negative numbers. Sets can't hold anti-items. If these are sets, then they do not contain "negative people". The cardinality of a set is always an ordinal number (for finite sets this is a natural number).

Nov 29th 2011, 11:13 AM

ehpoc

Re: Cardinalities and ultimate sets

Well then I have no clue what is going on. Everyone is telling me this problem is impossible then?!?!?

Nov 29th 2011, 04:57 PM

Annatala

Re: Cardinalities and ultimate sets

Quote:

Originally Posted by ehpoc

Well then I have no clue what is going on. Everyone is telling me this problem is impossible then?!?!?

Yes. It's impossible because it gives you equations that produce a negative result for one of the sets. Even if sets could hold "fewer than zero" elements, which they cannot, if negative numbers are allowed in the Venn then determining all of the values would require more data than you're given.

It is probably just a typo in the problem. There aren't supposed to be negative people, and you would have enough information to determine what you need if the numbers were right. Email your instructor already.